Problem: Simplify the following expression: $y = \dfrac{q}{10} - \dfrac{3q}{5}$
Answer: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10$ and $5$ $\lcm(10, 5) = 10$ $ y = \dfrac{1}{1} \cdot \dfrac{q}{10} - \dfrac{2}{2} \cdot \dfrac{3q}{5} $ $y = \dfrac{q}{10} - \dfrac{6q}{10}$ $y = \dfrac{q -6q}{10}$ $y = \dfrac{-5q}{10}$ Simplify the expression by dividing the numerator and denominator by 5: $y = \dfrac{-q}{2}$